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Small time asymptotics of Ornstein-Uhlenbeck densities in Hilbert spaces. (English) Zbl 1196.60055

Summary: We show that S. R. S. Varadhan’s [Commun. Pure Appl. Math. 20, 431–455 (1967; Zbl 1055.16503)] small time asymptotics for densities of the solution of a stochastic differential equation in \(R^{n}\) carries over to a Hilbert space-valued Ornstein-Uhlenbeck process whose transition semigroup is strongly Feller and symmetric. In the Hilbert space setting, densities are with respect to a Gaussian invariant measure.

MSC:

60F99 Limit theorems in probability theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Citations:

Zbl 1055.16503
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